Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C4×D83 | C2 | semidirect |
| 3. #19127577 | C2 | semidirect |
| 4. #19127562 | C2 | semidirect |
| 5. #19127557 | C2 | semidirect |
| 6. #379×C83 | C2 | semidirect |
| 9. C22×C22⋊D83 | C4 | semidirect |
| 12. C22×C4×D83 | C22 | semidirect |
| 14. C2×C22⋊Dic83 | C22 | semidirect |
| 15. C2×(C2×D83)⋊C4 | C22 | semidirect |
| 17. C83⋊#95 | C22 | semidirect |
| 20. C2×C22⋊C4×C83 | C22 | semidirect |
| 28. C2×C22⋊D83 | C2×C4 | semidirect |
| 30. C22×Dic83 | C2×C4 | semidirect |
| 40. C24×C83 | C2×C4 | semidirect |
| 60. C22×D83 | C22⋊C4 | semidirect |
| 99. C83 | #2308 | semidirect |
| 105. #379 | D83 | semidirect |
| 118. C2×C22⋊C4 | C2×D83 | semidirect |
| 126. C24 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D83 | 2 |
| C2×C22⋊C4×D83 | 2 |
| #19127577 | 2 |
| #19127562 | 2 |
| #19127557 | 2 |
| #379×C83 | 2 |
| #2308 | 83 |